Method for manufacturing a hollow rack shaft

ABSTRACT

A hollow rack shaft is manufactured through a first step, a second step and a third step. At the first step, the plate-like workpiece of substantial rectangular shape is press formed into a gutter-like shape. The first die set used at this step is provided with slant die surfaces for canceling elastic recovering generated at the workpiece when the workpiece is removed from the first die set. At the second step, a row of rack teeth is press-formed on the flat bottom portion of the workpiece formed in the first step. The die set used at the second step is provided with a recess for releasing surplus workpiece material within the die clearance at a stroke end of the pressworking. At the third step, each of a pair of legs of the workpiece is bent in a semi-circular shape so as to be butted to each other. At this time, a mandrel is inserted between the legs of the workpiece.

[0001] This invention is based on Patent Applications No. 2000-64298,No. 2000-114306 and No. 2000-114502 filed in Japan, the contents ofwhich are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] This invention relates to a hollow rack shaft, and moreparticularly to a method for manufacturing a hollow rack shaft for asteering system used in an automobile.

[0004] 2. Description of the Related Art

[0005] In the case of a rack-and-pinion type steering system for anautomobile frequently used in an automobile industry, the rotation of asteering wheel operated by a driver is transmitted to a pinion. Therotation of this pinion is transmitted to a rack shaft engaged with thepinion and this is converted into a motion in a lateral direction (alongitudinal direction of the rack). Since the rack shaft is connectedto the steering rod, the direction of front wheels is changed by alateral motion of the rack shaft. Since such a steering mechanism asdescribed above is well known in the art, further description will beeliminated.

[0006] The aforesaid rack shaft has been attained by gear cutting on asolid, namely not hollow, material. In recent years, as alreadydescribed in Japanese Laid-Open Patent No. Hei 6-246379, JapaneseLaid-Open Patent No. Sho 58-218339 (Japanese Patent Publication No. Hei4-028582) and Japanese Laid-Open Patent No. Hei 11-180318, fuelefficiency of an automobile has been improved by making a hollow rackshaft to attain the lightweightization of the rack shaft.

[0007] A manufacturing method for forming rack is disclosed in JapaneseLaid-Open Patent No. Hei 6-246379, which describes that a tube materialis inserted into a first forming split die, a primary forming is carriedout, then, the aforesaid primary formed material is inserted into asecondary forming split die having, at a part of its inner surface,teeth corresponding to the rack teeth, a semi-circular mandrel is pressfitted at one end of it.

[0008] A manufacturing method disclosed in Japanese Laid-Open Patent No.Sho 58-218339 describes that a die having teeth corresponding to therack teeth is pushed to a tube material to form rack teeth under thestate that a mandrel is inserted into the tube material surrounded withfixed die.

[0009] The manufacturing method disclosed in Japanese Laid-Open PatentNo. Hei 11-180318 is an invention invented by Mr. Ohkubo, one of theinventors of the present invention. The manufacturing method comprisesthe following first to third steps. At the first step, a plate-likematerial having a substantial rectangular shape as original one is bentinto a gutter shape along a center of longitudinal direction. At thistime, the central part of the gutter-shaped member is formed into a flatbottom section, and both the side portions are formed into asemi-circular shape having legs therein. At the second step, the rackteeth are plastically formed at the flat bottom portion. At the thirdstep, the gutter-shaped material is bent such that the legs of thecentral part and the both sides are abutted to each other, and then ahollow rack shaft is formed.

[0010] In the case disclosed in the first two gazettes above, the holloworiginal workpiece is applied as the material, while, in the casedisclosed in the third gazette (the gazette of Japanese Laid-Open PatentNo. Hei 11-180318), a flat plate workpiece is applied in place of thehollow workpiece, so that the third manufacturing method has some meritsin view of material cost, transportation cost and storing cost. Further,according to the third manufacturing method, it is avoidable to giveeach portion except a tooth bottom portion an excessive thickness inorder to maintain the tooth bottom portion at a required wall thickness.Then, the rack shaft can be sufficiently light in its weight.

SUMMARY OF THE INVENTION

[0011] However, it has become apparent that the manufacturing methoddisclosed in the gazette of Japanese Laid-Open Patent No. Hei 11-180318has some problems not considered up to now as described below.

[0012] Although, in general, almost the deformation applied to the workpiece by a plastic working operation gives a permanent deformation,temporary deformation, i.e. elastic deformation remains in a part ofdeformation. As the lead applied by the die is removed, the elasticdeformation remaining at each minute element in the workpiece isrestored and it is transferred to a new balanced state where each of theforces of the other fine elements keeps its balance. Due to this fact,after the workpiece is removed from the die, the entire workpiece doesnot take a shape coinciding with the die and its shape deviates fromthat of the die. In particular, in the case that a degree of forming iswidely different in reference to each of the locations at the workpiece,this deviation shows a large value.

[0013]FIGS. 1a to 1 c show the state when the flat plate workpiece isformed into a gutter-like shape at the first step of the prior artmanufacturing method (the final stage of press stroke). In this case,FIG. 1a is a front sectional view for showing a workpiece and a die.FIG. 1b is a sectional view taken along line B-B of FIG. 1a. FIG. 1c isa sectional view taken along line C-C of FIG. 1a. The die set at thefirst step comprises an upper die set 110 including a right upper die111, a left upper die 112 and a central upper die 113; and a lower dieset 120 including a right lower die 121, a left lower die 122 and acentral lower die 123. As apparent from these figures, a workpiece W isformed by the lower die set 120 and the upper die set 110 into agutter-like shape having a flat bottomed central portion 2 a, a racktooth not-yet formed, and having semi-circular bottomed portions 1extending from the both sides of the flat bottomed central portion 2 a.

[0014] Upon completion of the first step, when the upper die set 110 islifted up to take out the workpiece W, the workpiece W takes a differentshape from that of the lower die set 120 and the upper die set 110. FIG.2 is a sectional view for showing the workpiece W expressed under thestate of releasing such a stress as above being exaggerated, as shown inthis figure, the workpiece W is warped like a bow with the bottom partof the gutter being placed inside, i.e. the opening of the legs beingplaced outside.

[0015] The reason why such a state occurs is as follows. The originalplate workpiece is formed into different shape at each potion,therefore, the degree of deformation given to each portion differs fromothers. Namely, the degree of deformation given to the flat bottomportion 2 a, the semicircular bottom portion 1 and the interface portion9 of the workpiece are different from each other. When the load appliedto the workpiece is unloaded.after plastic working, each portionrecovers elastically in correspondingly different manner. Hence theworkpiece warps like a bow.

[0016] Further, a similar problem may also occur at the second step ofthe prior art manufacturing method. FIG. 3 is a sectional view forshowing the workpiece W and the dies when rack teeth 2 b are formed atthe portion 2 a (FIG. 2) at the second step. The die set at the secondstep comprises an upper die set 210 including a right upper die 211, aleft upper die 212 and a central upper die 213; and a lower die set 220including a right lower die 221, a left lower die 222 and a centrallower die 223. The upper surface of the central lower die 223 is formedwith teeth complementary shape to the rack teeth to be formed. Inaddition, the lower surface of the central upper die 213 is providedwith a corrugated shape corresponding to the rack teeth at the surface.

[0017] The rack teeth unformed portion 2 a of the workpiece W is formedrack teeth by approaching the central lower die 223 and the centralupper die 213 to each other under the state that the semi-circular part1 of the workpiece W is held between the right upper die 211, the rightlower die 221 and between the left upper die 212 and the left lower die222.

[0018] Since many teeth are formed at the rack portion 2 b the degree offorming at each location is different. When the workpiece W is removedfrom the die upon completion of the second step, the workpiece Wsometimes shows unintended deformation by the same cause as above. FIG.4 illustrates one example of the workpiece W in which deformationappeared, in this case, the workpiece W is warped like a bow shape withthe bottom part of the gutter being set inside i.e. with the openingpart of the leg being set outside.

[0019] Even if the third step for butting legs is applied to theworkpiece W which has unintended deformation after the second step, thisdeformation remains, so that as shown in FIG. 5 as its exaggerated form,the workpiece W having unintended deformation, for example, a bow-shapedwarp is attained. The workpiece having such a warp as above cannot beused as a rack shaft as it is.

[0020] At the second step of the prior art manufacturing method, anotherproblem differing from the aforesaid problem may occur. FIGS. 6a and 6 bare a front sectional view and a sectional view taken along line B-B toillustrate this problem. It should be noted that these figures areillustrated in inverse relation in a vertical orientation against theaforesaid figures. In addition, side clamping dies 203 are auxiliarydies for clamping the workpiece W from side surfaces to prevent theworkpiece W from being moved.

[0021] As already described above, rack teeth are formed by the centralupper die 213 and the central lower die 223. These dies are designedsuch that the volume of the clearance composed of two dies is slightlylarger than the volume of the workpiece W placed in the clearance whenthe central upper die 213 and the central lower die 223 approach mostduring forming of rack teeth.

[0022] However, in the case that the workpiece W is thicker than theintended thickness or, in the case that a volume of the aforesaidminimum clearance is smaller than the intended volume due to an error instroke of a press machine, the pressure at this clearance becomes quitehigh. Due to this fact, a quite high load is applied to the centralupper die 213 and the central lower die 223, and in particular, the loadis concentrated at either the cavity 5 a or 5 b. These excessive load orfatigue of die material caused by repeated application of the load maygenerate a crack 5 (or damage) in dies 213, 223 as shown in FIG. 6a.

[0023] In addition, when the rack teeth are formed, a quite large amountof material must be flown near the teeth ends of the workpiece W, inparticular, a crack 5 may easily be generated at either the cavity 5 aor 5 b.

[0024] Further, at the third step of the prior art manufacturing method,another problem differing from the aforesaid problem is generated. FIGS.7a to 7 c, FIGS. 8a to 8 c and FIGS. 9a to 9 c are views forillustrating processes in which the hollow rack shaft is formed bybending both legs of the workpiece W so as to be butted to each other.FIG. 7a, FIG. 8a and FIG. 9a are front sectional views. FIG. 7b, FIG. 8band FIG. 9b are sectional views taken along line B-B in the frontsectional views. FIG. 7c, FIG. 8c and FIG. 9c are sectional views takenalong line C-C in each of the front sectional views, respectively.

[0025] At first, as shown in FIGS. 7a to 7 c, the workpiece W formed therack teeth at the second step is supported on the lower die set 320including the left lower die 322, the central lower die 323 and theright lower die 321. In addition, a pair of side lower dies 324 arearranged at the both sides of the central lower die 323 and they supportthe side lower portion of the workpiece W. The upper surfaces of thesedies have such a shape that the workpiece W passed through the secondstep is well fitted. In addition, the upper die 310 has, at its lowerpart, a semi-circular concave surface having a diameter that isapproximately the same as a clearance at the legs of the workpiece W.

[0026] Then, when the upper die 310 descends, both legs 6 of theworkpiece W are guided by the semi-circular concave surface and start todeform under application of bending force directed inwardly. At thistime, although a high bending moment is applied near the roots of thelegs 6, only a low bending moment is applied to the location near theextremity ends of the legs 6. Due to this fact, as shown in FIGS. 8b and8 c, deformation progresses only at the location near the roots of thelegs 6 and the portions near the extremity ends of the legs 6 arescarcely deformed.

[0027] Due to this fact, as shown in FIGS. 9a to 9 c, even if the upperdie 310 descends down to the stroke end, a linear portion 7 undeformedinto an arc shape remains near the extremity ends of the legs 6. As aresult, since the sectional shape is not a true circle, the finishedrack shaft becomes an inferior product. Further, since the butted endsurfaces are not properly faced to each other, the end surfaces areinclined to form a V-shaped groove, so that they may become hindrancewhen a welding such as a laser welding and the like is performed.

[0028] It is required that a cylindrical shape without strain is formedby smoothly connecting the semi-circular bottom portion formed at thefirst step and the back arc portion formed at the third step, so thatsuch a rack shaft as above is repaired by cutting or grinding operationor it is wasted as an improper product.

[0029] If it is assumed that the rack shaft having a deformedcylindrical part and the deformed semi-circular portion of the rack isattained, the grinding margin at the subsequent grinding step must havea large amount in order to correct this deformed sectional shape into aright circular shape. This process may become a problem that not onlyincreasing manufacturing cost but also decreasing strength of the rackshaft as grinding margin increases, as a result, the rack shaft isdamaged or its lifetime is shortened. If the thickness of the originalplate member is made thicker in compliance with the grinding margin toprevent a reduction in strength, other portion of the completed hollowrack shaft becomes thicker than required, so that this may become aproblem that the product may not satisfy the required weight reduction.

[0030] This invention aims at resolving these problems, and in thisinvention, a hollow rack shaft is manufactured through the first step,second step and third step, respectively. At the first step, asubstantially rectangular plate workpiece is formed into a gutter-likeshaped workpiece by press-forming. The gutter-like shaped workpiece hasa bottom portion and a pair of leg-like side walls extending from theside edges of the bottom portion and substantially in parallel from eachother. The bottom portion comprises a substantial flat bottom portion ata central portion in a longitudinal direction and semi-circular bottomportions at both outer sides. At the second step, a row of rack teeth ispress-formed at the aforesaid flat bottom portion of the workpiece. Atthe third step, each of the pair of leg-like sidewalls of the workpieceformed at the second step is bent into a semi-circular shape to bebutted to each other.

[0031] At the first step of this invention, further the first die set isused, wherein the first die set is provided with a surface such ascomplementary shape to each of the two semi-circular bottom portions inthe gutter-like shape, and the surface such as the complementary shapeis inclined to eliminate elastic deformation generated at the workpiecewhen the workpiece is removed from the first die set.

[0032] At the one second step in this invention, the second die set isused, the second die set is provided with a die surface such ascomplementary shape to a row of rack teeth formed at the flat bottomportion, the surface such as the complementary shape also has a shapefor canceling elastic deformation of this workpiece when the workpieceis removed from the second die set.

[0033] At another second step of this invention, the second die set isused, the second die set is provided with a die surface such ascomplementary shape to a row of rack teeth formed at the flat bottomportion, a part of the die surface such as complementary shape isprovided with recess for releasing the surplus material of the workpiecein the die clearance at the stroke end of the press-forming. The seconddie set can be divided into a plurality of segments at the location ofrecess. The recess is located at a position where a protrusion formed bythe recess does not interfere with a pinion engaged with the rack.

[0034] The other second step of this invention comprises a preliminaryforming step and a main forming step, wherein at the preliminary formingstep, a row of teeth, having substantially the same pitch as the pitchof a row of rack teeth finally formed and having a smaller pressureangle than a pressure angle of the rack teeth finally formed, is formed.And at the main forming step, a row of teeth formed at the preliminaryforming step is reformed into a row of rack teeth having required rackteeth shape. Further, at the main forming step, a part of the diesurface is provided with a recess for releasing surplus material of theworkpiece in the die gap, and it is possible to use the die set composedof a plurality of segments divided at the location of the aforesaidrecess.

[0035] A third step in this invention is executed such that a mandrel,having at a part thereof a cylindrical outer surface corresponding to ahollow inner surface of the rack shaft, is inserted between theaforesaid pair of leg-like sidewalls. Further, this mandrel comprises atleast two separable segments in such a way that it can be pulled out ofthe hollow rack shaft upon completion of the third step.

[0036] Other objects and advantages besides those discussed above shallbe apparent to those skilled in the art from the description of apreferred embodiment of the invention which follows. In the description,reference is made to accompanying drawings, which form a part thereof,and which illustrates an example of the invention. Such example,however, is not exhaustive of various embodiments of the invention, andtherefore reference made to the claims which follow by the descriptionfor determining the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings, which are incorporated in andconstitute a part of the specification, illustrate embodiments of theinvention and together with the description, serve to explain theprinciples of the invention.

[0038]FIGS. 1a to 1 c show the state when the flat plate workpiece isformed into a gutter-like shape at the first step of the prior artmanufacturing method.

[0039]FIG. 1a is a front sectional view for showing a workpiece and adie.

[0040]FIG. 1b is a sectional view taken along line B-B of FIG. 1a.

[0041]FIG. 1c is a sectional view taken along line C-C of FIG. 1a.

[0042]FIG. 2 is a sectional view for showing the state of the workpieceunder releasing of such a stress as found in the prior art.

[0043]FIG. 3 is a sectional view for showing a workpiece and dies whenthe rack teeth are formed at the portion 2 a at the second step of theprior art.

[0044]FIG. 4 is a sectional view for showing one example of theworkpiece that deformation appears upon completion of the first step inthe prior art.

[0045]FIG. 5 is a sectional view for showing an example of the workpiecethat deformation shown in FIG. 4 remains even after the third step inthe prior art.

[0046]FIGS. 6a and 6 b illustrate an example in the prior art that acrack is generated at the die, and they are a front sectional view and asectional view taken along line B-B.

[0047]FIGS. 7a to 7 c, FIGS. 8a to 8 c and FIGS. 9a to 9 c are views forillustrating processes that the hollow rack shaft is formed by bendingboth legs of the workpiece W so as to be butted to each other.

[0048]FIG. 7a, FIG. 8a and FIG. 9a are front sectional views. FIG. 7b,FIG. 8b and FIG. 9b are sectional views taken along line B-B in each ofthe figures. FIG. 7c, FIG. 8c and FIG. 9c are sectional views takenalong line C-C in each of the front sectional views.

[0049]FIG. 10 is a front elevation sectional view for showing a state atthe time when a flat plate workpiece is formed into a gutter-like shapeat the first step of the method of this invention.

[0050]FIG. 11 is a front elevation sectional view for showing aworkpiece upon completion of the first step in which a bow-like warp ofthe workpiece is prevented by applying an inclination angle a to the diein this invention.

[0051]FIG. 12 is a front elevation sectional view for showing a statethat a rack tooth forming at the second step in this invention isfinished.

[0052]FIG. 13 is a front elevation sectional view for showing theworkpiece having no warp attained at the second step of this invention.

[0053]FIG. 14 is a front elevation sectional view for showing the dieset used in the second step of this invention and the workpiece W formedby this die set.

[0054]FIG. 15 is an enlarged sectional view for showing the workpiecewhich was formed protrusions f1 and f2 corresponding to a recess e.

[0055] FIGS. 16 to 18 are front elevation sectional views for showingthe die set and the workpiece in this invention to illustrate a state inwhich a second step is divided into a preliminary forming step and amain forming step.

[0056]FIG. 19 is a front elevation sectional view for showing an examplein this invention that the central lower die for the major forming atthe second step is divided.

[0057]FIGS. 20a to 22 c illustrate the third step of this inventionusing a mandrel.

[0058]FIGS. 20a, 21 a and 22 a are front elevation sectional views.

[0059]FIGS. 20b, 21 b and 22 b are sectional views taken along line B-Bof each of the figures.

[0060]FIGS. 20c, 21 c and 22 c are sectional views taken along line C-Cof each of the figures.

[0061]FIG. 23 is an outer appearance view for showing the completedhollow rack shaft in this invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0062] Now, preferred embodiments of the present invention will hedescribed in detail while referring to the accompanying drawings.

[0063] In the preferred embodiments shown in the following description,the hollow rack shaft is manufactured through a first step, a secondstep and a third step. That is, the original plate-like workpiece ofsubstantial rectangular shape is bent into a gutter-like shape along acenter of longitudinal direction. At this time, the central portion ofthe workpiece is formed into a flat bottom and its both sides are formedinto a semi-circular shape having legs. At the second step, the rackteeth are formed at the central portion of the flat bottom by plasticmachining. At the third step, the leg-like side walls are bent such asthe edges of the walls are butted each other, and then a hollow rackshaft is formed. In this way, this invention is not different from theprior art manufacturing method in view of the fact that the method formanufacturing the hollow rack shaft in these preferred embodimentscomprises three steps, although this invention is substantiallydifferent from the prior art manufacturing method in regard to thecontent of each of the steps. Due to this fact, in order to avoidoverlapped description about the content already described, only thedifferent points will be described.

First Embodiment

[0064]FIG. 10 is a longitudinal sectional view for showing a state atthe time when a flat plate workpiece is formed into a gutter-like shape(a final end of a press stroke) at the first step of the method of thisinvention. In the same manner as that of the prior art, at the time tocomplete the first step, the plate workpiece W has a flat bottom at itscentral portion, and the workpiece is formed into a gutter-like shapeincluding unformed flat portion 602 a to form rack teeth at the secondstep and a semi-circular portion 601 having a semi-circular bottom part.Then, the die set used for this operation is also similar to that of theprior art. Namely, the die set comprises an upper die set 610 includinga right upper die 611, a left upper die 612 and a central upper die 613;and a lower die set 620 including a right lower die 621, a left lowerdie 622 and a central lower die 623.

[0065] However, this invention is different from the prior art in viewof the fact that the die surfaces of the right upper die 611, the leftupper die 612, the right lower die 621 and the left lower die 622corresponding to the bottom of the semi-circular portion 601 areinclined by a proper inclination angle α. Applying the properinclination angle α to these dies, the bow-like warp of the workpiece Wand the inclination angle α, as shown in FIG. 2, are canceled eachother, and the bottom portions of the two semi-circular portions 601 arearranged on one line as shown in FIG. 11 when the workpiece W is takenout from the die set. A value of the inclination angle α is adjustedaccording to workpiece material and the sizes (length, width andthickness) of the workpiece W, respectively, so that the mostappropriate value is selected on the basis of trial-and-error.

[0066] A bow-like warp at the workpiece W generated at the second step,already described, can also be canceled by the same method as above.FIG. 12 is a view for showing the case that the rack teeth are formed atthe second step onto the gutter-like workpiece W formed at the firststep (or the gutter-like workpiece W formed at the first step in theprior art) , and it illustrates when the step has been completed. Then,the die set used at the second step comprises an upper die set 710including a right upper die 711, a left upper die 712 and a centralupper die 713; and a lower die set 720 including a right lower die 721,a left lower die 722 and a central lower die 723.

[0067] Rack teeth and corrugation are formed at the rack teeth unformedportion 602 a by the central upper die 713 and the central lower die723. As already described, in order to cancel a bow-like warp of theworkpiece W generated at this time, an inclination angle β is applied toeach of the die surfaces corresponding to the bottom portion of thesemi-circular portion 601 of each of the right upper die 711, left upperdie 712, right lower die 721 and left lower die 722, respectively. Theappropriate inclination angle β is attained on the basis of atrial-and-error by similar way to the first embodiment.

[0068] As shown in the first embodiment, at the first step or the secondstep, the bow-like warp generated by the elastic recovering of theworkpiece W when the workpiece W is removed from the die set can besubstantially canceled, as shown in FIG. 13, by applying either theinclination angle α or β to the die set. Due to this fact, anyparticular working step for correcting the bow-like warp is eliminatedand the hollow rack shaft can be manufactured at a low cost.

Second Embodiment

[0069] At the second step of the second preferred embodiment, the diesurface is provided with a recess for releasing an excessive increasingin pressure in the die clearance at the stroke end of the pressworking.FIG. 14 is a longitudinal section for showing a die set 803 including acentral upper die 813 and a central lower die 823 used in the secondstep, and the workpiece W formed by this die set. It should be notedthat FIG. 14 to FIG. 19 are different from FIG. 1 in view of the factthat the upper or lower side of the workpiece W is in reverse state.

[0070] Each of the central upper die 813 and the central lower die 823is a split type die composed of a plurality of segments 813S, 823S.Symbols 813D, 823D denote their dividing lines. The extremity end of thesegment 823S has a shape corresponding to one surface of rack teeth andforms one rack tooth with the same shape of another adjoining segment823S. Similarly, the extremity end of the segment 813S is provided witha shape corresponding to the inside of the rack teeth and forms a shapesimilar to one tooth shape with the same shape of another adjoiningsegment 813S. Each of the central upper die 813 and the central lowerdie 823 is provided with a recess e, wherein this recess e is arrangedto pass through the dividing lines 813D, 823D. Accordingly, each recesse is positioned at the rack tooth or at the tooth bottom part of shapesimilar to the tooth shape.

[0071] When the rack teeth are formed by the central upper die 813 andthe central lower die 823 having such recess e as above, if the materialof the workpiece W within the die clearance at the stroke end of thepressworking is excessive, the material flows into the recess e, as aresult, it is possible to prevent the pressure within the die clearancefrom being excessively increased. Thereby it is possible to prevent thedie from being damaged or cracked. Then, at this time, protrusions f1,f2 indicated in FIG. 15 are formed at the location corresponding to therecess e of the workpiece.

[0072] Since the protrusion f2 formed at the rack teeth side is formedat the location opposing against the tooth bottom of a pinion when rackteeth are engaged with the pinion p, a sufficient large clearance d isestablished there in view of design. Therefore, there is no possibilitythat the protrusion f2 becomes the hindrance which comes in contact withthe pinion p in gear transmission. Since the protrusion f1 is placed atan opposite side of the rack teeth, it does not become a hindrance ingear transmission.

[0073] The second step is divided into two steps, i.e. a preliminaryforming step and a main forming step to prevent the die from beingdamaged. FIGS. 16 and 18 are longitudinal sections for showing the dieset and the workpiece W when the preliminary forming step and mainforming step have been completed. In addition, FIG. 17 is a longitudinalsection between the die set and the workpiece W indicating the initialstate of the main forming step.

[0074] The preliminary forming process is carried out by the die set 903including the central lower die 923 and the central upper die 913. Atthe preliminary forming, an intermediate shape to reach to the finalshape is formed. The teeth formed by the central lower die 923 in thepreliminary forming process are not narrowed at the upper end as thefinal rack tooth shape. Describing in more detail, the tooth thickness Aat the tooth end is slightly thinner than the tooth thickness B at thetooth root. The best shape is that the tooth has the taper that thetooth end thickness A is thinner than the root B, in order to remove theworkpiece W easily from the central lower die 923 after the preliminarystep has been completed. The pressure angle is smaller than the finaltooth shape.

[0075] The tooth thickness A and the tooth thickness B are designedthinner than a tooth size of rack teeth of the product. It is desirablethat the plate thickness t at the tooth root portion is established assame as that of the tooth root of the product. The phase and pitch areestablished as same as those of the rack teeth of the product. The toothshape formed in the preliminary forming step is optional except theirpitch and phase.

[0076] This preliminary forming process is a simple forming process, sothat the material easily flows, a load to the die set 903 can beremarkably reduced as compared with that of forming the rack teeth inone step.

[0077] As shown in FIGS. 17 and 18, in the main forming process, a dieset 1003 for the main forming process composed of a central lower die1023 having a complementary shape to the shape of the product rack.Since the workpiece is already formed to an approximately near shape tothe final product by the preliminary forming step, the requisitematerial flow is less in its volume and the load applied to the die canbe substantially reduced.

[0078] The dies 913, 923, 1013 and 1023 shown in FIGS. 16 to 18 can bedivided into segments. FIG. 19 shows an example in which the die set1003 for the main forming process is composed of the central lower die1023 and the central upper die 1013; each of dies 1023 and 1013comprises a plurality of segments 1023S and a plurality of segments1013S, respectively.

[0079] In the second embodiment, a die load can be reduced by flowingthe excessive material into the recess e. The die load is also reducedby dividing die into a plurality of segments at the location of therecess, and further dividing the second step into two steps.

Third Embodiment

[0080] The aforesaid problem of the third step in the prior art, thatis, the back surface of the rack shaft cannot be formed into a truecircle is resolved by using the mandrel as shown in FIGS. 20a to 22 c.FIGS. 20a, 21 a and 22 a are front elevation sectional views; FIGS. 20b,21 b and 22 b are sectional views taken along line B-B in each of thefront elevation sectional views; and FIGS. 20c, 21 c and 22 c aresectional views taken along line C-C in each of the front elevationsectional views. The same reference symbols in FIGS. 7a to 9 c are usedexcept for the symbol 112 of the mandrel are used in these figures.

[0081] The workpiece W formed with rack teeth upon completion of thesecond step is placed on the lower die set 320. At this time, as shownin FIGS. 20a to 20 c, the workpiece W is placed such that two legs 6 arefaced up. The upper surface of the central lower die 323 iscomplementary to the rack tooth shape, and each of the rack teeth isfitted to this complementary rack tooth surface. The upper surface ofeach of the right lower die 321 and the left lower die 322 has acircular shape as the lower surface of the workpiece W is well fitted.

[0082] A mandrel set 112 is inserted between the two legs 6. The mandrelset 112 comprises two members or segments to intend such that eachmember can be pulled out after they are butted to each other. One ofthem comprises a central D-shaped portion 112 b and a circular portion112 a extending from the former, and the other comprises only a circularportion. Since any composition is acceptable if the mandrel set 112 canbe pulled out after operation, it is also possible that it is dividedinto three members of two circular portions and one D-shaped portion, orit can be divided into two symmetrical segments at the central part ofthe D-shaped portion.

[0083] Then, as the upper die 310 descends, both legs 6 of the workpieceW are guided at the semi-circular concave surface, receive a bendingforce directed inwardly, start its deformation. At this time, a highbending moment is applied to a location near the roots of the legs 6 atthe beginning and a small bending moment is merely applied to thelocation near the extremity ends of the legs 6. However, since themandrel set 112 exists, the part where the largest bending moment isapplied moves along the cylindrical outer surface gradually from theroots of the legs 6 toward the extremity end portions of the legs 6. Themiddle of the state is shown in FIGS. 21a to 21 c and the final state isshown in FIGS. 22a to 22 c. In this way, the back surface of the rackshaft is formed into a circular shape.

[0084] After this operation, when the upper die 310 ascends, a slightclearance is formed between the mandrel set 112 and the workpiece W byan unavoidable spring-back of the workpiece W, resulting in that themandrel set 112 can be easily pulled out. After this operation, sincethe slight opened butted portions can be closed by a quite low force,they are welded under the closed state by laser welding, for example.Even if this rack shaft is finished and ground, a mere slight grindingmargin is required and the strength of the rack shaft is notsubstantially reduced by grinding operation.

[0085] Although only preferred embodiments are specifically illustratedand described herein, it will be appreciated that many modifications andvariations of the present invention are possible in light of the aboveteachings and within the purview of the appended claims withoutdeparting from the spirit and intended scope of the invention.

What is claimed is:
 1. A method for manufacturing a hollow rack shaftcomprising: a first step for forming a substantially flat andrectangular plate workpiece into a gutter-like shaped workpiece; saidgutter-like shaped workpiece has a flat bottom portion, a pair ofsemi-circular bottom portion extending from each longitudinal side ofsaid flat bottom portion and a pair of leg-like side wall extendingupwardly in parallel from each lateral side of said flat bottom portionand said semi-circular portions; a second step for forming a row of rackteeth on said flat bottom portion of said gutter-shaped workpiece; and athird step for forming said workpiece into a hollow shape by bendingsaid leg-like side walls by butting edges of said walls each other;wherein a surface of a die set used in said first step is inclined inlongitudinal direction of said workpiece so as to cancel elasticrecovering of said workpiece when said workpiece is removed from saiddie set.
 2. A method for manufacturing a hollow rack shaft comprising: afirst step for forming a substantially flat and rectangular plateworkpiece into a gutter-like shaped workpiece; said gutter-like shapedworkpiece has a flat bottom portion, a pair of semi-circular bottomportion extending from each longitudinal side of said flat bottomportion and a pair of leg-like side wall extending upwardly in parallelfrom each lateral side of said flat bottom portion and saidsemi-circular portions; a second step for forming a row of rack teeth onsaid flat bottom portion of said gutter-shaped workpiece; and a thirdstep for forming said workpiece into a hollow shape by bending saidleg-like side walls by butting edges of said walls each other; wherein adie set used in said second step provides a complementary surface to arow of rack teeth formed on said flat bottom portion and said surfacepreviously provides a shape to cancel elastic recovering of saidworkpiece when said workpiece is removed from said die set.
 3. A die setused in a method for manufacturing a hollow rack shaft, said methodcomprising; a first step for forming a substantially flat andrectangular plate workpiece into a gutter-like shaped workpiece; saidgutter-like shaped workpiece has a flat bottom portion, a pair ofsemi-circular bottom portion extending from each longitudinal side ofsaid flat bottom portion and a pair of leg-like side wall extendingupwardly in parallel from each lateral side of said flat bottom portionand said semi-circular portions; a second step for forming a row of rackteeth on said flat bottom portion of said gutter-shaped workpiece; and athird step for forming said workpiece into a hollow shape by bendingsaid leg-like side walls by butting edges of said walls each other;wherein, a die set used in said second step provides a complementarysurface to said semi-circular bottom portion and a surface of said dieset is inclined in longitudinal direction of said workpiece so as tocancel elastic recovering of said workpiece when said workpiece isremoved from said die set.
 4. A die set used in a method formanufacturing a hollow rack shaft, said method comprising; a first stepfor forming a substantially flat and rectangular plate workpiece into agutter-like shaped workpiece; said gutter-like shaped workpiece has aflat bottom portion, a pair of semi-circular bottom portion extendingfrom each longitudinal side of said flat bottom portion and a pair ofleg-like side wall extending upwardly in parallel from each lateral sideof said flat bottom portion and said semi-circular portions; a secondstep for forming a row of rack teeth on said flat bottom portion of saidgutter-shaped workpiece; and a third step for forming said workpieceinto a hollow shape by bending said leg-like side walls by butting edgesof said walls each other; wherein a die set used in said second stepprovides a complementary surface to a row of rack teeth formed on saidflat bottom portion and said surface previously provides a shape tocancel elastic recovering of said workpiece when said workpiece isremoved from said die set.
 5. A method for manufacturing a hollow rackshaft comprising: a first step for forming a substantially flat andrectangular plate workpiece into a gutter-like shaped workpiece; saidgutter-like shaped workpiece has a flat bottom portion, a pair ofsemi-circular bottom portion extending from each longitudinal side ofsaid flat bottom portion and a pair of leg-like side wall extendingupwardly in parallel from each lateral side of said flat bottom portionand said semi-circular portions; a second step for forming a row of rackteeth on said flat bottom portion of said gutter-shaped workpiece; and athird step for forming said workpiece into a hollow shape by bendingsaid leg-like side walls by butting edges of said walls each other;wherein a surface of a die set used in said second step is provided witha plurality of recesses for releasing surplus material of said workpiecein a die clearance at a stroke end of press-forming.
 6. A die set usedin a method for manufacturing a hollow rack shaft, said methodcomprising; a first step for forming a substantially flat andrectangular plate workpiece into a gutter-like shaped workpiece; saidgutter-like shaped workpiece has a flat bottom portion, a pair ofsemi-circular bottom portion extending from each longitudinal side ofsaid flat bottom portion and a pair of leg-like side wall extendingupwardly in parallel from each lateral side of said flat bottom portionand said semi-circular portions; a second step for forming a row of rackteeth on said flat bottom portion of said gutter-shaped workpiece; and athird step for forming said workpiece into a hollow shape by bendingsaid leg-like side walls by butting edges of said walls each other;wherein, a surface of said die set used in said second step is providedwith a plurality of recesses for releasing surplus material of saidworkpiece in a die clearance at a stroke end of press-forming.
 7. A dieset according to claim 6, wherein, each die of said die set is dividedinto a plurality of segments at said recesses.
 8. A die set according toclaim 7, wherein, said recess is located at a position where aprotrusion formed by said recess does not interfere with a pinionengaged with said rack.
 9. A die set according to claim 6, wherein, saidrecess is located at a position where a protrusion formed by said recessdoes not interfere with a pinion engaged with said rack.
 10. A methodfor manufacturing a hollow rack shaft comprising: a first step forforming a substantially flat and rectangular plate workpiece into agutter-like shaped workpiece; said gutter-like shaped workpiece has aflat bottom portion, a pair of semi-circular bottom portion extendingfrom each longitudinal side of said flat bottom portion and a pair ofleg-like side wall extending upwardly in parallel from each lateral sideof said flat bottom portion and said semi-circular portions; a secondstep for forming a row of rack teeth on said flat bottom portion of saidgutter-shaped workpiece; and a third step for forming said workpieceinto a hollow shape by bending said leg-like side walls by butting edgesof said walls each other; wherein, said second step further comprises apreliminary forming step and a main forming step; at said preliminaryforming step, a row of intermediate rack teeth substantially equal tothe finally required pitch and smaller than the finally requiredpressure angle is formed; and at said main forming step, a row of rackteeth with required tooth shape is formed.
 11. A method according toclaim 10, wherein, a surface of said die set used in said main formingstep is provided with a plurality of recesses for releasing surplusmaterial of said workpiece in a die clearance at a stroke end; and eachdie of said die set is divided into a plurality of segments at saidrecess.
 12. A method for manufacturing a hollow rack shaft comprising: afirst step for forming a substantially flat and rectangular plateworkpiece into a gutter-like shaped workpiece; said gutter-like shapedworkpiece has a flat bottom portion, a pair of semi-circular bottomportion extending from each longitudinal side of said flat bottomportion and a pair of leg-like side wall extending upwardly in parallelfrom each lateral side of said flat bottom portion and saidsemi-circular portions; a second step for forming a row of rack teeth onsaid flat bottom portion of said gutter-shaped workpiece; and a thirdstep for forming said workpiece into a hollow shape by bending saidleg-like side walls by butting edges of said walls each other; wherein,said third step is executed with inserting a mandrel with a semicircularupper half portion.
 13. A mandrel used in a method for manufacturing ahollow rack shaft, said method comprising: a first step for forming asubstantially flat and rectangular plate workpiece into a gutter-likeshaped workpiece; said gutter-like shaped workpiece has a flat bottomportion, a pair of semi-circular bottom portion extending from eachlongitudinal side of said flat bottom portion and a pair of leg-likeside wall extending upwardly in parallel from each lateral side of saidflat bottom portion and said semi-circular portions; a second step forforming a row of rack teeth on said flat bottom portion of saidgutter-shaped workpiece; and a third step for forming said workpieceinto a hollow shape by bending said leg-like side walls by butting edgesof said walls each other; wherein said mandrel is provided with asemicircular upper half portion and is inserted between said leg-likeside walls when said third step is executed.
 14. A mandrel according toclaim 12, wherein said mandrel is divided into two segments or more sothat said segments are removed from said hollow rack shaft after saidthird step is executed.